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I have a square with the following four corner points:

(0, 0),(100 0),(100 100),(0, 100).

The square is then rotated clockwise ten degrees.

What is the formula that will allow me to determine its new location?

Thanks.

Narasimham
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jb3330421
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  • First line here: http://en.wikipedia.org/wiki/Rotation_matrix – The Chaz 2.0 Jan 07 '15 at 22:27
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    You must specify the center (i.e., the fixed point) of the rotation for this question to make sense. Is the center of rotation the origin $(0,0)$? Is it the center of the square $(50,50)$? – MPW Jan 07 '15 at 22:45
  • hi, yes, it is being rotated at the center, 50,50.. – jb3330421 Jan 07 '15 at 22:58

1 Answers1

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Move the square so that it's center is the origin $(0, 0)$. This means moving all points with the vector $(-50, -50)$.

As complex numbers, the points would be $p_1=-50+50i$, $p_2=50+50i$, $p_3=50-50i$, $p_4=-50-50i$. These points can be rotated 10°(=$\frac{\pi}{18}rad$) clockwise by multiplying them with $e^{\frac{\pi*i}{18}}$. The points (complex numbers) that you then end up with should be moved back by reversing the movement we did in the first step (move all points (50, 50)).

I have no calculator with support for complex numbers here, so you will have to do the actual calculations yourself.

Dasherman
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